Solve the inequality 4x - 2 ≥ 6.

Solve the inequality 4x - 2 ≥ 6.

• A. x ≥ 2
• B. x ≥ 1
• C. x ≤ 2
• D. x > 2

Answer: (A)

Solving a linear inequality works like solving an equation, but you keep the inequality sign the same whenever you multiply or divide by a positive number. Start by moving the constant to the other side: add 2 to both sides to get 4x ≥ 8. Then divide by 4, a positive number, so the inequality direction stays the same: x ≥ 2. This means all numbers that are 2 or larger satisfy the inequality. For a quick check, x = 2 gives 4(2) − 2 = 6, which is equal to 6, and x = 1 gives 4(1) − 2 = 2, which is not as large as 6, so it doesn’t work. The solution set is x ≥ 2. The option stating x is at least 2 is the correct description. The others would include values that don’t satisfy the inequality or miss the equality case at 2.

Solving a linear inequality works like solving an equation, but you keep the inequality sign the same whenever you multiply or divide by a positive number. Start by moving the constant to the other side: add 2 to both sides to get 4x ≥ 8. Then divide by 4, a positive number, so the inequality direction stays the same: x ≥ 2. This means all numbers that are 2 or larger satisfy the inequality. For a quick check, x = 2 gives 4(2) − 2 = 6, which is equal to 6, and x = 1 gives 4(1) − 2 = 2, which is not as large as 6, so it doesn’t work. The solution set is x ≥ 2. The option stating x is at least 2 is the correct description. The others would include values that don’t satisfy the inequality or miss the equality case at 2.